CAT LRDI Questions PDF (Truth Lie Concept and DI Sets)

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CAT Truth Lie Concept and DI Sets Questions PDF
CAT Truth Lie Concept and DI Sets Questions PDF

CAT LRDI Questions PDF (Truth Lie Concept Questions and DI Sets)

LRDI Truth Lie Concept & DI (Data Interpretation) are some of the important topics in the CAT LRDI Section. LR Truth Lie Concept questions are interesting to solve, and not very difficult if you learn the basics and practice them well. Questions on DI sets, and Truth Lie Concept are asked in the CAT. You can expect a few questions from LR Truth Lie Concept in the latest format of the CAT LRDI section. This article will look into some important CAT LRDI Questions PDF (such as Truth Lie Concept Questions & also a few DI sets) for CAT LRDI section. If you want to practice these important LR Truth Lie Concept questions, you can download the PDF below, which is completely Free.

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Instructions

Read the following passage and answer the questions that follow.

An audit unearthed a financial scam in NWC Corporation. One or more among the 9 financial accountants of NWC Corporation are suspected to have fudged the accounts. Following are the statements made by the nine suspects.
Shrinivas: Nagraj fudged the accounts
Datta: Shrinivas did not fudge the accounts
Nagraj: Datta is lying and I did not fudge accounts
Jose: Shrinivas is telling the truth
Samuel: Exactly three of the suspects are telling the truth
Ejaz: Datta is lying and Shrinivas fudged the accounts
Chaudhary: Datta fudged the accounts
Ganeshan: Datta is lying and Shrinivas is telling the truth
Panda: Samuel is lying

Question 1: If Samuel is telling the truth, which of the following statements is true?

a) Chaudhury and Datta are telling the truth

b) Nagraj fudged the accounts

c) Chaudhury and Jose are telling the truth

d) Shrinivas and Datta are telling the truth

e) Shrinivas fudged the account

1) Answer (A)

Solution:

It is given that Samuel is telling the truth. So, there must be exactly three truth tellers including Samuel.
If Samuel is telling the truth, Panda must be lying.

Case I
Let us assume that Shrinivas is telling the truth and Nagraj fudged the accounts.. In this case, Jose must also be telling the truth. So, everybody except Samuel, Shrinivas and Jose must be lying. However, Datta’s statement is also true and thus there are more than three truth tellers. So, our assumption is wrong. Thus, Shrinivas must be lying and Nagraj did not fudge the accounts. Also, Jose and Ganeshan must be lying as both says that Shrinivas is telling the truth

Case II
Let us assume that Datta is telling the truth and Shrinivas did not fudge the accounts. In this case, Nagraj and Ezaz must be lying as they say that Datta is lying. So, we have already got six liers and thus, Chaudhary must be telling the truth. Therefore, our assumption is valid.

Case III
Let us assume that Datta is not telling the truth. In this case Nagraj and Ezaz can be telling the truth along with Samuel and the other six guys must be lying. This case is also possible.

Except the above cases, any other case is not possible.

Therefore, option A is true in case II.Hence, option A is the correct answer.

Question 2: P, Q, R and S are four statements. Relation between these statements is as follows.
I. If P is true, then Q must be true.

II. If Q is true, then R must be true.

III. If S is true, then either Q is false or R is false.

Which of the following must be true?

a) If P is true, then S is false

b) If S is false, then Q must be true

c) If Q is true, then P must be true

d) If R is true, then Q must be true

2) Answer (A)

View Video Solution

Solution:

Options B,C and D are given vice-versa to given statements which is not necessarily true.

But according to option A, P is true, then Q and R will be true too but S will be false as for S, either Q or R should be false.

So answer will be A.

Question 3: Saira, Mumtaz and Zeenat have a ball, a pen and a pencil, and each girl has just one object in hand. Among the following statements, only one is true and the other two are false.
I. Saira has a ball.
II. Mumtaz does not have the ball.
III. Zeenat does not have the pen.
Who has the ball?

a) Saira

b) Mumtaz

c) Zeenat

d) Cannot be determined

3) Answer (B)

View Video Solution

Solution:

Assume the first statement is true. So, Saira has the ball. The other two statements are false. But if Saira has the ball, the statement that Mumtaz does not have the ball is true. But that statement should be false. Therefore, the first statement cannot be true.

Assume the second statement is true. So, Mumtaz does not have the ball. Also, since the other two statements are false, Saira also does not have the ball. So, Zeenat has the ball. But the third statement “Zeenat does not have a pen” becomes true in this case, which is incorrect. So, the second statement also cannot be true.

The only possibility is the statement has to be true. So, the second statement is false => Mumtaz has the ball.

Question 4: While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the counter and ran out. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really did not want to help Balbir. So each of them made a statement which contained one truth and one lie.
. Shopkeeper number 1 said: “The dog had black hair and a long tail.”
. Shopkeeper number 2 said: “The dog had a short tail and wore a collar.”
. Shopkeeper number 3 said: “The dog had white hair and no collar.”
Based on the above statements, which of the following could be a correct description?

a) The dog had white hair, short tail and no collar

b) The dog had white hair, long tail and a collar

c) The dog had black hair, long tail and a collar

d) The dog had black hair, long tail and no collar

4) Answer (B)

View Video Solution

Solution:

We know that  Shopkeeper 1 said: “The dog had black hair and a long tail.”. Lets consider the first part as false and other as true. So we have – dog didn’t have black hair and the dog had a long tail. Shopkeeper 2 said: “The dog had a short tail and wore a collar.” Here first part has to be false and other consequently will be true. So the dog wore a collar. Shopkeeper 3 said: “The dog had white hair and no collar.” Here 2nd part has to be false and hence 1st part has to be true. Thus, our first assumption satisfies all required conditions. Hence, in this case, we have – The dog had white hair, long tail and a collar. Hence option b.

Instructions

XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively

Question 5: The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be x and the number of orders delivered the day after be y. Then the average time to deliver order is $\frac{(x+2y)}{(x+y)}$. On which of the following days was the average time taken to deliver orders booked the least?

a) 15th

b) 13th

c) 14th

d) 16th

5) Answer (C)

View Video Solution

Solution:

The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5

Similarly we can find the orders booked on that day till 14th.

Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1

Similarly, the number of orders lost till 17th can be found out.

Number
of orders delivered on 13th are 11 out of which 4 are orders which were
booked in 11th so, 7 must be the orders which were booked on 12th.

Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.

Now, total number of orders booked on 12th will be 7+6+1=14.

FRom the table we can determine that among options, number of orders booked on 13th are maximum.

Average time can be calculated as follows

14 is the least

Question 6: The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on that day which are delivered on the second day after booking. On which of the following days, was the delivery ratio the highest?

a) 15th

b) 16th

c) 13th

d) 14th

6) Answer (D)

View Video Solution

Solution:

The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5

Similarly we can find the orders booked on that day till 14th.

Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1

Similarly, the number of orders lost till 17th can be found out.

Number
of orders delivered on 13th are 11 out of which 4 are orders which were
booked in 11th so, 7 must be the orders which were booked on 12th.

Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.

Now, total number of orders booked on 12th will be 7+6+1=14.

From the table we can determine that among options, number of orders booked on 13th are maximum.

For 15 the delivery ratio = 8/8 = 1

For 16 the delivery ratio = 13/10 = 1.3

For 13 the delivery ratio = 21/8 = 2.625

For 14 the delivery ratio = 15/3 = 5

Hence Option D

Checkout: CAT Free Practice Questions and Videos

Question 7: On which of the following days was the number of orders booked the highest?

a) 12th

b) 15th

c) 13th

d) 14th

7) Answer (C)

View Video Solution

Solution:

The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5

Similarly we can find the orders booked on that day till 14th.

Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1

Similarly, the number of orders lost till 17th can be found out.

Number
of orders delivered on 13th are 11 out of which 4 are orders which were
booked in 11th so, 7 must be the orders which were booked on 12th.

Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.

Now, total number of orders booked on 12th will be 7+6+1=14.

The total number of orders placed on 13th = 21+8+2 = 31

FRom the table we can determine that among options, number of orders booked on 13th are maximum.

Question 8: Among the following days, the largest fraction of orders booked on which day was lost?

a) 15th

b) 16th

c) 13th

d) 14th

8) Answer (A)

View Video Solution

Solution:

The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5

Similarly we can find the orders booked on that day till 14th.

Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1

Similarly, the number of orders lost till 17th can be found out.

Number of orders delivered on 13th are 11 out of which 4 are orders which were booked in 11th so, 7 must be the orders which were booked on 12th.

Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.

Now, total number of orders booked on 12th will be 7+6=1=14.

Fraction of orders booked on 15th that were lost = 12/28

Fraction of orders booked on 16th that were lost = 2/25

Fraction of orders booked on 13th that were lost =2/31

Fraction of orders booked on 14th that were lost = 8/30.

.’. Option A is correct answer.

Instructions

In a certain board examination, students were to appear for examination in five subjects:
English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations.

The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations.

If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations.

The following facts are also known.
I. Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.
II. The student who missed the Mathematics examination did not miss any other examination.
III. One of the students who missed the Hindi examination did not miss any other examination. The other student who missed the Hindi examination also missed the Science examination.

Question 9: For how many students can we be definite about which examinations they missed?

9) Answer: 4

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl missed his Mathematics examination.

Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.

Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi’s English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.

For Esha: best 3 out of 4 – 85(Hindi), 95(Mathematics), 60(Science)

Avg. = 240/3 = 80 which matches the given value

$\therefore\ $ Esha most likely missed her English examination.

For Foni: best 3 out of 4 – 78(Mathematics), 83(Social Science), 88(Science)

Avg. = 249/3 = 83 which matches the given value

$\therefore\ $ Foni most likely missed her English examination.

Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.

For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.

We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.

For Bithi: Best 2 out 3 – 90(English), 80(Hindi)

Avg = 170/2 = 85 which matches the given value

$\therefore\ $ Bithi is likely to have missed her Science and Social Science examinations.

We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.

Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).

Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):

Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi

Except for Alva and Deep, we can conclusively comment of the missed subjects of the rest four. Hence, the correct answer is 4.

Question 10: How many out of these six students missed exactly one examination?

10) Answer: 3

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl missed his Mathematics examination.

Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.

Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi’s English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.

For Esha: best 3 out of 4 – 85(Hindi), 95(Mathematics), 60(Science)

Avg. = 240/3 = 80 which matches the given value

$\therefore\ $ Esha most likely missed her English examination.

For Foni: best 3 out of 4 – 78(Mathematics), 83(Social Science), 88(Science)

Avg. = 249/3 = 83 which matches the given value

$\therefore\ $ Foni most likely missed her English examination.

Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.

For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.

We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.

For Bithi: Best 2 out 3 – 90(English), 80(Hindi)

Avg = 170/2 = 85 which matches the given value

$\therefore\ $ Bithi is likely to have missed her Science and Social Science examinations.

We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.

Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).

Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):

Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi

Hence, the correct answer to this question is 3. {Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi)}

Question 11: What BEST can be concluded about the students who missed the Science examination?

a) Bithi and one out of Alva and Deep

b) Alva and Bithi

c) Deep and Bithi

d) Alva and Deep

11) Answer (A)

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl missed his Mathematics examination.

Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.

Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi’s English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.

For Esha: best 3 out of 4 – 85(Hindi), 95(Mathematics), 60(Science)

Avg. = 240/3 = 80 which matches the given value

$\therefore\ $ Esha most likely missed her English examination.

For Foni: best 3 out of 4 – 78(Mathematics), 83(Social Science), 88(Science)

Avg. = 249/3 = 83 which matches the given value

$\therefore\ $ Foni most likely missed her English examination.

Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.

For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.

We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.

For Bithi: Best 2 out 3 – 90(English), 80(Hindi)

Avg = 170/2 = 85 which matches the given value

$\therefore\ $ Bithi is likely to have missed her Science and Social Science examinations.

We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.

Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).

Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):

Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi

Hence, the correct answer to this question is Option A: Bithi & one out of Alva and Deep.

Question 12: What BEST can be concluded about the students who did not appear for the Hindi examination?

a) Deep and Esha

b) Alva and Deep

c) Alva and Esha

d) Two among Alva, Deep and Esha

12) Answer (B)

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl missed his Mathematics examination.

Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.

Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi’s English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.

For Esha: best 3 out of 4 – 85(Hindi), 95(Mathematics), 60(Science)

Avg. = 240/3 = 80 which matches the given value

$\therefore\ $ Esha most likely missed her English examination.

For Foni: best 3 out of 4 – 78(Mathematics), 83(Social Science), 88(Science)

Avg. = 249/3 = 83 which matches the given value

$\therefore\ $ Foni most likely missed her English examination.

Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.

For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.

We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.

For Bithi: Best 2 out 3 – 90(English), 80(Hindi)

Avg = 170/2 = 85 which matches the given value

$\therefore\ $ Bithi is likely to have missed her Science and Social Science examinations.

We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.

Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).

Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):

Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi

Hence, the correct answer to this question is Option B: Alva and Deep.

Question 13: Which students did not appear for the English examination?

a) Carl and Deep

b) Cannot be determined

c) Alva and Bithi

d) Esha and Foni

13) Answer (D)

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl missed his Mathematics examination.

Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.

Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi’s English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.

For Esha:  best 3 out of 4 – 85(Hindi), 95(Mathematics), 60(Science)

Avg. = 240/3 = 80 which matches the given value

$\therefore\ $ Esha most likely missed her English examination.

For Foni: best 3 out of 4 – 78(Mathematics), 83(Social Science), 88(Science)

Avg. = 249/3 = 83 which matches the given value

$\therefore\ $ Foni most likely missed her English examination.

Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.

For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.

We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.

For Bithi: Best 2 out 3 – 90(English), 80(Hindi)

Avg = 170/2 = 85 which matches the given value

$\therefore\ $ Bithi is likely to have missed her Science and Social Science examinations.

We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.

Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).

Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):

Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi

Hence, the correct answer to this question is Option D: Esha and Foni.

Question 14: Who among the following did not appear for the Mathematics examination?

a) Alva

b) Carl

c) Foni

d) Esha

14) Answer (B)

View Video Solution

Solution:

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores.

For Alva: best 3 out of 4 – 80(English), 75(Hindi), 75(Science)

Avg. = 230/3 = 76.67 $\ne\ $ 70

For Carl: best 3 out of 4 – 80(Hindi), 90(Social Science), 100(Science)

Avg. = 270/3 = 90 which matches the given value

$\therefore\ $ Carl most likely missed his Mathematics examination.

For Foni: best 3 out of 4 – 83(English), 83(Social Science), 88(Science)

Avg. = 254/3 = 84.67 $\ne\ $ 78

Hence, we observe that only Carl has missed his Mathematics examination. Hence, Option B is the correct answer.

Instructions

Answer the questions with the given information and the data.

The following table gives number of T-Shirts sold (in thousand units) in Delhi and Mumbai. The T-Shirts are sold in different styles (S1, S2, S3, and S4) with different colours as shown in the table.

Question 15: From the combinations given below, which one has minimum difference in units sold across cities of Delhi and Mumbai ?

a) Red – S2

b) Green – S2

c) Yellow – S1

d) Black – S3

15) Answer (D)

Solution:

Red S2 = |70 – 89| = 19

Green S2 = |89-70| = 19

Yellow S1 = |50-69| = 19

Black S3 = |76-94| = 18.

Option (d) , Black S3 is the correct answer.

Question 16: If the profit margin of T-Shirts of various styles S1, $2, S3 and S4 are = 100, ¥ 100, ¥ 120 and & 120 respectively, then among the colour an city combinations given below, which combination has the maximum profit ?

a) Red-Mumbai

b) Red-Delhi

c) Green-Delhi

d) Blue-Mumbai

16) Answer (C)

Solution:

Red – Mumbai = 100*(76+89) + 120*(65+81)=34020

Red – Delhi     = 100 *(76+70) + 120*(70 + 95) = 34400

Green – Delhi =  100*(71+89) + 120*(92+65)  = 36040

Blue – Mumbai = 100*(94+64) +  120*(75+74) = 33680.

Maximum profit is with Green- Delhi

Question 17: Which style T-Shirt has highest difference in number of units sold between twocities of Delhi and Mumbai?

a) S1

b) S2

c) S3

d) S4

17) Answer (D)

Solution:

S1- Delhi = 507        ;   S1- Mumbai = 543      ; Difference = 36

S2-Delhi =  506        ;   S2 – Mumbai=560        ; Difference = 54

S3 – Delhi =515         ; S3 – Mumbai = 154        ; Difference = 1

S4 – Delhi = 496         ; S4 – Mumbai =  554       ; Difference = 58.

Option D, S4 is the correct answer.

Question 18: The average sales of which colour T-Shirt sold is same in both the cities ?

a) Yellow

b) Blue

c) Black

d) Red

18) Answer (D)

Solution:

Yellow – Delhi : 70.75             ;      Yellow – Mumbai : 66.

Blue – Delhi     : 83.25             ;      Blue – Mumbai    :76.75

Black – Delhi    :67                  ;       Black – Mumbai  :92.5

Red –  Delhi      :77.75             ;      Red – Mumbai      :77.75.

Red has same average sales in both cities

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